Wave Nature of Matter

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which

(a) an electron, and

(b) a neutron, would have the same de Broglie wavelength.

An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength ______.

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be:

Matter waves are ______.

Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.

Calculate the momentum of the electrons accelerated through a potential difference of 56 V.

Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc², where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

1. λ = 10 nm
2. λ = 10^–1 nm
3. λ = 10^–4 nm
4. λ = 10^–6 nm